Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10604652 | C2 | semidirect |
| 4. #10604623 | C2 | semidirect |
| 6. #10598597 | C2 | semidirect |
| 7. #10598589 | C2 | semidirect |
| 20. C5×#476 | C4 | semidirect |
| 21. #65380 | C4 | semidirect |
| 22. #65296 | C4 | semidirect |
| 25. #65140 | C4 | semidirect |
| 149. #476 | AGL(1,𝔽5) | semidirect |
| 387. C5 | #9207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617153 | 2 |
| #10612790 | 2 |
| #10604652 | 2 |
| #10604623 | 2 |
| #10604421 | 2 |
| #10598597 | 2 |
| #10598589 | 2 |
| #9207 | 5 |